Answer: y = (1/12)x^2 - 2
Explanation:
The equation of a parabola in vertex form is given by:
y = a(x-h)^2 + k
where (h,k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.
In this case, the vertex is given as (0, -2), so h = 0 and k = -2. Also, the parabola passes through the point (6, 1), which means that when x = 6, y = 1. We can use this information to solve for "a".
Substituting the values of h, k, x, and y in the equation, we get:
1 = a(6-0)^2 - 2
Simplifying this equation, we get:
1 + 2 = 36a
3 = 36a
a = 3/36
a = 1/12
Now that we know the value of "a", we can substitute it in the vertex form equation to get the final equation of the parabola:
y = (1/12)(x-0)^2 - 2
Simplifying this equation, we get:
y = (1/12)x^2 - 2
Therefore, the equation of the parabola in vertex form is y = (1/12)x^2 - 2.